Public-Key Cryptography Based on a Cubic Extension of the Lucas Functions

One of the goals of public-key cryptography is to securely exchange a key by use of a public channel without the users previously communicating with one another. In 1976 W. Diffie and M. Hellman had an idea how to do this by exploiting mathematically difficult one-way problems. Diffie-Hellman key exchange is based on the believed difficulty of the discrete log problem. This paper presents a new key exchange protocol based on functions that were developed to generalize the Lucas functions. Relevant results about this generalization of the Lucas functions are provided that provide the machinery for the Diffie-Hellman-like key exchange presented here. Lastly, there is a brief discussion about the efficiency of our system versus Diffie-Hellman key exchange and LUCDIF.